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%I #10 Mar 25 2024 09:53:59
%S 0,1,1,2,5,9,16,32,61,114,219,418,792,1510,2878,5473,10421,19847,
%T 37776,71917,136931,260680,496278,944847,1798804,3424569,6519790,
%U 12412480,23631034,44989208,85651217,163064109,310444213,591028898,1125210433
%N Expansion of (x+x^3+x^5)/(1-x-3*x^3-x^5).
%C a(n) is the number of 231-avoiding permutations of length n that have order 1 or 3.
%H Amanda Burcroff and Colin Defant, <a href="https://arxiv.org/abs/1907.09451">Pattern-Avoiding Permutation Powers</a>, arXiv:1907.09451 [math.CO], 2019.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,3,0,1).
%F G.f.: (1-x+x^2)*(1+x+x^2)/(1-x-3*x^3-x^5).
%K easy,nonn
%O 0,4
%A _Colin Defant_, Jul 23 2019
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